We consider a cellular neural network (CNN) with a bias term z in the integer lattice Z on the plane R2. We impose a symmetric coupling between nearest neighbors, and also between next-nearest neighbors. Two parameters, a and ε, are used to describe the weights between such interacting cells. We study patterns that can exist as stable equilibria. In particular, the relationship between mosaic p...

The paper describes an image matching method based on visual attention and SURF keypoints. Biologically inspired visual attention system is used to guide local interest point detection. Interest points are represented with SURF descriptors. One–to–one symmetric search is performed on descriptors to select a set of matched interest point pairs. Pairs are then weighted according to attention dist...

We study generalized restricted Boltzmann machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as generalized Hopfield models. We underline the role of the retrieval phase for both inference and learning processes and we show that ret...

For computing the recurrent component, let us first consider the case of symmetric additive learning, when reciprocal connections are perfectly correlated. In this case, the probability P(W|x) can be written as ∏ i,j δ(Wij ,Wji) · N (W/,μ/,C/), where the subscript / marks the fact that the multivariate normal is defined in the space of the weights from the upper triangular part of matrix W. Wri...

we characterize strictly diagonal type of embeddings offinitary symmetric groups in terms of cardinality and the characteristic. namely, we prove thefollowing.let $kappa$ be an infinite cardinal. if$g=underset{i=1}{stackrel{infty}bigcup} g_i,$ where $ g_i=fsym(kappa n_i)$,$(h=underset{i=1}{stackrel{infty}bigcup}h_i, $ where $ h_i=alt(kappa n_i) ), $ is a group of strictly diagonal type and$xi=(...

2 Mercure model Mercure is an information retrieval system based on a connexionist approach and modeled by a multi-layered network. The network is composed of a query layer (set of query terms), a term layer (representing the indexing terms) and a document layer [Boughanem99]. Mercure includes the implementation of a retrieval process based on spreading activation forward and backward through t...

Abstract. We construct a full strongly exceptional collection in the triangulated category of graded matrix factorizations of a polynomial associated to a non-degenerate regular system of weights whose smallest exponents are equal to −1. In the associated Grothendieck group, the strongly exceptional collection defines a root basis of a generalized root system of sign (l, 0, 2) and a Coxeter ele...

The theoretical and practical framework of Field Programmable Neural A rr ays has been de ned to reconcile simple hardware topologies with complex neural architectures: FPNAs lead to powerful neural models whose original data exchange scheme allows to use hardware-friendly neural topologies. This paper addresses preliminary results in the study of the computation pow er of FPNAs. The computatio...

The van Lint-Wilson AB-method yields a short proof of the Roos bound for the minimum distance of a cyclic code. We use the AB-method to obtain a different bound for the weights of a linear code. In contrast to the Roos bound, the role of the codes A and B in our bound is symmetric. We use the bound to prove the actual minimum distance for a class of dual BCH codes of length q2− 1 over Fq. We gi...

We define a block-reduced version of the crystal graph of spin representations of the symmetric and alternating groups, and separate it into layers, each obtained by translating the previous layer and, possibly, adding new defect zero blocks. We demonstrate that each layer has weight-preserving central symmetry, and study the sequence of weights occurring in the maximal strings. The Broué conje...